What is a "generalized" machine learning algorithm?
Actually you have used 2 terminologies there:


The first one is that  Machine Learning algorithm results can be "generalised". This refers to how well your trained Machine Learning model will perform on previously unseen data (test set or implemented on field). This is particularly not easy as data trends may change over time resulting in loss of accuracy. There are various methods to implement this like (having a cross validation set and a test set, which comes under the broad scheme of k-fold cross validation)
The second you mentioned is '"generalised" algorithms, routines or functions'. Most Machine Learning algorithms can be applied to a broad range of problems. For example the training of a NN is generally done by backprop which is universally applied to all NN's. Similarly, you can use CNN to find features of local interest (i.e. local dependencies) in anything that can be represented in a pictorial form (strings of DNA). Also combinations of CNN and RNN are being used to solve many problems. Thus, only a basic generalised algorithm is being applied to a lot of problems. NOTE: I have never seen any one use it in this context, but practically it happens.


Here are a few resources for general reading purposes (not mathematical):


Overfitting and Underfitting With Machine Learning Algorithms
Generalization and Overfitting